On the well-posedness of the inverse nodal problem (Q2764817)

Let \(x_k^{(n)}\), \(0<x_1^{(n)}<\ldots<x_{n-1}^{(n)}<1\), be the nodal points of the \(n\)th eigenfunction of the Sturm-Liouville operator \(H\): NEWLINE\[NEWLINE Hy=-y''+q(x)y,\quad q(x)\in L(0,1), NEWLINE\]NEWLINE NEWLINE\[NEWLINE y(0)\cos\alpha + y'(0)\sin\alpha =0,\quad y(1)\cos\beta + y'(1)\sin\beta =0. NEWLINE\]NEWLINE Here, the inverse nodal problem of recovering \(H\) from the given nodal set \(\{x_k^{(n)}\}\) is considered. The authors study the well-posedness of the inverse nodal problem, i.e., the existence, uniqueness and stability of solutions to this inverse problem.